We report scanning tunneling microscopy observations, which imply that all
atoms in a close-packed copper surface move frequently, even at room
temperature. Using a low density of embedded indium `tracer' atoms, we
visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms
seem to make concerted, long jumps. Responsible for this motion is an ultra-low
density of surface vacancies, diffusing rapidly within the surface. This
interpretation is supported by a detailed analysis of the displacement
distribution of the indium atoms, which reveals a shape characteristic for the
vacancy mediated diffusion mechanism that we propose.Comment: 4 pages; for associated movie, see
  http://www-lion.leidenuniv.nl/sections/cm/groups/interface/projects/therm

E. Somfai

F. Besenbacher

H. A. van der Vegt

H.-C. Jeong

J. B. Hannon

J. W. M. Frenken

K. Morgenstern

L. Kuipers

M. Breeman

M. J. A. M. Brummelhuis

M. S. Hoogeman

R. van Gastel

S. B. van Albada

W. van Saarloos

Z. Zhang

English

arXiv

Crossref

Physical Review Letters

Nothing Moves a Surface: Vacancy Mediated Surface Diffusion

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Saarloos, W. van

Gastel, R. van

Somfai, E.

Albada, S.B. van

Frenken, J.W.M.

Leiden University Scholary Publications

VOLUME 86, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 19 FEBRUARY 20011562Nothing Moves a Surface: Vacancy Mediated Surface DiffusionR. van Gastel,1 E. Somfai,2 S. B. van Albada,1 W. van Saarloos,2 and J. W. M. Frenken11Kamerlingh Onnes Laboratory, Universiteit Leiden, P.O. Box 9504, 2300 RA Leiden, The Netherlands2Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands(Received 8 September 2000)We report scanning tunneling microscopy observations, which imply that all atoms in a Cu(001)surface move frequently, even at room temperature. Using a low density of embedded indium “tracer”atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to makeconcerted, long jumps. Responsible for this motion is an ultralow density of surface vacancies, diffusingrapidly within the surface. This interpretation is supported by a detailed analysis of the displacementdistribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusionmechanism that we propose.DOI: 10.1103/PhysRevLett.86.1562 PACS numbers: 68.35.Fx, 05.40.Fb, 07.79.Cz, 66.30.LwAtomic rearrangements on low-index surfaces are oftenthought to predominantly take place at steps, which serveas sources and sinks for adatoms. The diffusion of adatomsalong or between steps leads to characteristic step fluctua-tions. Also adatom and vacancy islands are known to movevia rearrangements at their perimeter. Many STM studieshave been devoted to the mobility of surfaces. Most ofthese have focused on the motion of steps [1–3], islands[4], or adsorbates [5]. Recently it has been proposed thatsurface vacancies are responsible for mass transport be-tween adatom islands on Cu(001) [6]. Unfortunately, thereare no experimental techniques available with both the spa-tial and the temporal resolution necessary to follow thediffusion of naturally occurring vacancies in a low-indexmetal surface.Indium which is deposited on Cu(001) has been foundto modify the epitaxial growth of copper on this sur-face. Its presence results in layer-by-layer growth insteadof rough three-dimensional growth [7]. After deposition,the indium atoms proceed to steps on the copper surface[8,9]. At temperatures just below room temperature theyare incorporated in the outermost layer on substitutionalterrace sites. In this study we have used indium atomsthat are embedded within the first layer of a Cu(001) sur-face to monitor the diffusion of surface atoms [10]. Ourobservations lead us to conclude that surface vacancies areresponsible for the mobility of the indium and that thislow-index metal surface is far from static, even at roomtemperature.The experiments were performed with a variable tem-perature scanning tunneling microscope (STM) [11] in ul-trahigh vacuum (UHV). A Cu single crystal of 99.999%purity was mechanically polished parallel to the (001)plane [12]. Prior to mounting the crystal in the UHV sys-tem we heated it in an ArH2 atmosphere to remove sul-fur impurities. The sample surface was further cleaned inUHV by several tens of cycles of sputtering with 600 eVAr ions and annealing to 675 K. After approximately ev-ery fifth cycle the surface was exposed to a few Langmuirof O2 to remove carbon from the surface. STM images0031-90070186(8)1562(4)$15.00showed a well-ordered surface with terrace widths up to8000 Å. Small quantities of indium were deposited on thesurface from a Knudsen cell.The starting point of the observations is shown in Fig. 1.At room temperature we have deposited 3% of a mono-layer of indium on the Cu(001) surface. The STM im-age shows a region around an atomic step, separating twoflat terraces of the copper surface. The image was taken42 min after deposition and shows that most indium atomsare within 150 Å from the step. From the apparent heightof 0.4 Å of the indium atoms, we infer that they are em-bedded within the first copper layer. What we know fromlower-temperature STM experiments is that a newly de-posited indium atom first “hops” over the surface until itencounters a step. At the step it enters the outermost cop-per layer (either on the upper or on the lower side of thestep), after which it diffuses away from the step, while re-maining embedded within the copper surface layer.FIG. 1. A 548 3 409 Å2 STM image of a step on a Cu(001)surface, taken 42 min after deposition of 0.03 ML of indium atroom temperature. Embedded indium atoms show up as brightdots. The image shows a high density of embedded indiumatoms near the step (It  0.1 nA, Vt  20.70 V).© 2001 The American Physical SocietyVOLUME 86, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 19 FEBRUARY 2001We follow the diffusion of the embedded indium atomsin the copper terrace by making a series of images of thesame area on the copper surface to form an STM movie ofthe motion [13]. To our initial surprise, we found that theindium atoms move via long jumps of more than a singlelattice spacing, separated by long time intervals [14]. In ad-dition, the movies show that there is a strong tendency fornearby indium atoms to jump at the same time. Figure 2illustrates this peculiar motion with a set of three imagestaken from a movie measured at 320 K. From the STMmovies we have measured the distribution of jump lengthsof the embedded indium atoms, which has been plotted inFig. 3. Note that there is a significant probability for theindium atoms to make jumps as far as five lattice spacings.The long jumps and the high probability of nearby in-dium atoms to jump simultaneously suggest strongly thatdiffusion of the indium is mediated by another particle,which diffuses so rapidly that it remains invisible to theSTM. The scenario that we propose is that the indiummoves over several lattice spacings during a multiple en-counter with a single assisting particle by changing placesseveral times with that particle. The two obvious candi-dates for this particle are adatoms (copper atoms on topof the surface layer) and vacancies (missing atoms in theoutermost copper layer). We can rule out the first possibil-ity on the basis of Fig. 1. If an indium atom were to changeplaces with an adatom, it would thereby become an adatomitself. We know from Fig. 1 and from other observationsthat indium adatoms rapidly hop over the outermost copperlayer to the steps, without entering the copper surface di-rectly. This means that if an embedded indium atom wouldtrade places with a copper adatom, it would immediatelydisappear from the STM image and reappear somewhereat the step, which is definitely not what we observe.Figure 4 illustrates how a single surface vacancy candisplace an atom in the outermost copper layer, either anindium or a copper atom, over several lattice spacings. Inthis mechanism, the length of the long jumps of the indiumatoms depends on the average number of times that a singleFIG. 2. Three 50 3 50 Å2 STM images selected from a moviemeasured at RT illustrating the unusual diffusion of embeddedindium atoms. In the time interval of 160 s between images(a) and (b), no diffusion of the embedded indium atoms hastaken place. In image (c), taken 20 s later, a diffusion eventhas taken place. Both indium atoms present in images (a) and(b) have moved over several lattice spacings and two more in-dium atoms have jumped into the imaged region (It  0.9 nA,Vt  20.58 V).vacancy changes places with an indium atom, and we as-sociate the frequency of the (long) indium jumps with thefrequency with which the indium is encountered by newvacancies. We have measured the distribution of time in-tervals between consecutive jumps (see Fig. 5). The wait-ing time distribution is purely exponential, from which weinfer that individual long jumps are uncorrelated in timeand are therefore caused by different vacancies, indepen-dently formed at random times. The fact that a single va-cancy will usually encounter various In atoms, naturallyexplains the tendency for nearby indium atoms to jump atthe same time.The fact that we never see individual vacancies in theSTM images and the fact that the STM movies do not re-solve the elementary steps in a multi-lattice-spacing jumpneed not surprise us. Using the embedded atom model(EAM), we estimate that the formation energy of a vacancyin the Cu(001) surface is 0.51 eV and that the activationenergy for a surface atom to exchange with the empty site,and thereby move the vacancy, amounts to 0.29 eV [15].Based on these estimates, we expect that at room tempera-ture only one surface atom out of roughly 6 3 109 is miss-ing, and that each empty site changes position with a highfrequency, on the order of 108 Hz. These numbers are typi-cal for low-index metal surfaces and illustrate why it is sodifficult to see the vacancy diffusion at all. At low tem-peratures, where vacancy motion would be slow enough tobe followed by an inherently slow instrument such as theSTM, the probability of finding a vacancy is hopelesslyclose to zero. At temperatures high enough for the surfaceto contain a sufficiently high density of vacancies, the va-cancies move much too fast to be imaged at all.In order to obtain a quantitative understanding of thejump vector distribution of the embedded indium atoms,we performed a numerical calculation as well as a con-tinuum approximation, according to the following model:FIG. 3. The distribution of jump vectors measured from STMmovies at 320 K. Plotted is the probability for jumps of anindium atom from its starting position to each of the shownnonequivalent lattice sites. To illustrate the unusual diffusionbehavior, the expected jump vector distribution for the case ofsimple hopping is plotted to the right.1563VOLUME 86, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 19 FEBRUARY 2001FIG. 4. An example diffusion event which leads to a multi-lattice spacing displacement of the indium atom. The indium-vacancy exchanges are marked in the figure with crosses toshow the pathway of the indium between its beginning and endpoints.The Cu(001) surface is a finite l 3 l square lattice, withcopper atoms at the lattice sites; the boundary of the latticecorresponds to the steps. One copper atom at the center ofthe lattice is replaced by indium, and a vacancy is releasedone atomic site next to it. The vacancy performs a biasedrandom walk, its hopping probabilities to the four differentdirections from each site are set from the diffusion barrierscalculated using the EAM potentials [15].The vacancy displaces the atoms in its path, includingthe indium atom. When the vacancy arrives at the bound-ary of the lattice, it is annihilated (it recombines at thesteps). At this moment the displacement of the indiumatom is evaluated, and the whole process is repeated forthe next vacancy to acquire the distribution of the In jumpvectors.For the case of equal diffusion barriers and infinite lat-tices, this problem has been solved analytically [16]. Al-though the results in some limits are quite similar to ourcontinuum solution (see below), the equal-barrier resultsare not directly applicable to the case of indium in copper.Instead of moving isotropically, the vacancy neighboringthe indium atom has a much stronger preference to jumptowards the indium than to other directions. On the basis0 5 10 15 20 25 30Waiting time (nr. of images)050100150200Frequencyτ = 4.5 ± 0.1 images= 8.5 ± 0.2 sFIG. 5. Time-interval statistics for subsequent jumps of indi-vidual indium atoms, measured from STM movies at 320 K witha time per image of 1.88 s. The dotted curve is an exponentialfit with a time constant t  8.5 s.1564of the values of the barriers, as calculated with the EAM,we estimate the direct return jump to be a factor of 106more probable than a jump in any of the other three di-rections. This difference has a significant impact on theindium jump distribution: the mean square displacementis about 2.23 larger than in the equal-barrier case, whilethe overall shape of the distribution is about the same [15].It is computationally beneficial to separate the motion ofthe vacancy from that of the indium atom. For the indiumatom, only the direction of the next return of the vacancyis of importance, rather than the vacancy path which leadsto it. Therefore it is enough to calculate the probabilities offirst return of the vacancy to the indium atom from the fourdifferent directions after it left the indium in one direction,as well as the probability of the vacancy’s recombinationbefore return. The In atom performs a random walk, wherethe direction of each step with respect to the previous oneis chosen according to these return probabilities, and aftereach step the walk terminates with the vacancy’s recombi-nation probability. This procedure yields the proper finaljump distribution, while giving up the time information,which is experimentally irrelevant anyway. (This approachis valid under the assumption that the environment of theindium does not change with the steps it takes, i.e., it isstill close to the middle of the lattice.)In practice, instead of using Monte Carlo– type methods,we enumerate the possible trajectories to obtain the returnprobabilities and the indium jump vectors; this provides su-perior convergence. The following numerical values werecalculated for T  320 K (EAM barriers) and for a latticesize l  401, which corresponds to the typical experimen-tal terrace width of 1000 Å. After leaving the indium atomto the right, the vacancy’s return probabilities from the fourdirections are the following: pright  1 2 2.4 3 1027,pup  pdown  1.1 3 1027, pleft  4.2 3 1029, and thevacancy recombines with probability prec  1.1 3 1028.These values depend very weakly on the lattice size l. Thefact that two dimensions is the marginal dimension for thereturn problem of a random walker implies a logarithmic ldependence of prec. The root mean square jump length ofthe In atoms is 3.5 nearest neighbor spacings. The full dis-tribution of the In jump lengths is plotted in Fig. 6 togetherwith the experimental values. The quantitative agreementsupports our interpretation of the mechanism of the indiumdiffusion.We now show that a simple continuum approach to thisproblem gives a quite good approximation to the jump sta-tistics. Let us denote the probability of “mobile indium”at position r with  r, n, where the counter n measuresthe number of times the vacancy returns to the In atom.The indium is considered “mobile” while the vacancy isstill around, and “immobile” after the vacancy has recom-bined. The effective diffusion equation for  r, n is≠r, n≠n Deff=2 2 e . (1)VOLUME 86, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 19 FEBRUARY 2001FIG. 6. The distribution of the jump lengths of the indiumatoms at 320 K. Filled circles correspond to the experimentalvalues, open circles are from the numerical calculation, and thesolid curve is the isotropic continuum (Bessel) approximation.For comparison, the dashed curve shows the best-fit Gaussiandistribution.The first term corresponds to the vacancy mediated dif-fusion of the mobile indium (isotropic, in this continuumapproach), and the second term to the recombination of thevacancy, which makes the indium immobile. The solutionin the case of Dirac-delta initial conditions at the origin is r, n 14pDeffne2r24Deffn2en. (2)We are interested in the final, immobile distributionof In:pr Z `0e r, n dn 12peDeffK0µrpDeffe∂,(3)where K0 is the modified Bessel function of order 0. Theparameters can all be calculated: e is the recombinationprobability prec of the vacancy, and the effective diffusioncoefficient Deff can be calculated from the return probabili-ties, as will be discussed in detail elsewhere [15]. Equa-tion (3) gives a good approximation of the jump lengthdistribution (Fig. 6), without any fitting parameter.Finally, we evaluate the resulting diffusion coefficientD for copper terrace atoms. Using numerical calculations,we calculate that the multiple encounter of a single vacancywith a copper atom in a clean copper surface results in aroot mean square displacement of the atom of 1.6 nearestneighbor spacings. Multiplying this number with the ob-served average jump rate of the embedded indium atoms(Fig. 5), we obtain D  0.42 Å2 ? s21.In conclusion, the diffusive motion of the indium atomscan be explained by the presence of a low density of ex-tremely mobile vacancies in the first layer of the surface.This interpretation is supported by the shape of the distri-bution of measured jump lengths. The root mean squarejump length can be reproduced accurately in calculationsif we take into account the chemical difference betweenthe indium and copper atoms. We conclude that terracesof low-index metal surfaces, such as Cu(001), cannot beconsidered as static, even at room temperature. The natu-rally occurring vacancies lead to a continuous reshufflingof the surface, as if it were an atomic realization of a slidepuzzle.We gratefully acknowledge B. Poelsema for help withthe preparation of the Cu crystal. This work is part ofthe research program of the “Stichting voor FundamenteelOnderzoek der Materie (FOM),” which is financially sup-ported by the “Nederlandse Organisatie voor Wetenschap-pelijk Onderzoek (NWO).”[1] H.-C. Jeong and E. D. Williams, Surf. Sci. Rep. 34, 171(1999).[2] Z. Zhang and M. G. Lagally, Science 276, 377 (1997).[3] L. Kuipers, M. S. Hoogeman, and J. W. M. Frenken, Phys.Rev. Lett. 71, 3517 (1993).[4] K. Morgenstern, G. Rosenfeld, B. Poelsema, andG. Comsa, Phys. Rev. Lett. 74, 2058 (1995).[5] F. Besenbacher, Rep. Prog. Phys. 59, 1737 (1996).[6] J. B. Hannon et al., Phys. Rev. Lett. 79, 2506 (1997).[7] H. A. van der Vegt et al., Phys. Rev. B 51, 14 806 (1995).[8] M. Breeman and D. O. Boerma, Phys. Rev. B 46, 1703(1992).[9] M. Breeman and D. O. Boerma, Surf. Sci. 287/288, 881(1993).[10] R. van Gastel, E. Somfai, W. van Saarloos, and J. W. M.Frenken, Nature (London) 408, 665 (2000).[11] M. S. Hoogeman et al., Rev. Sci. Instrum. 69, 2072 (1998).[12] R. J. I. M. Koper, Surface Preparation Laboratory,http://www.surface-prep-lab.com[13] For the full movie please visit http://www-lion.leidenuniv.nl/groups/ip[14] STM observations show qualitatively similar motion of Pdatoms in the Cu(001) surface, B. S. Swartzentruber (privatecommunication).[15] R. van Gastel et al. (to be published).[16] M. J. A. M. Brummelhuis and H. J. Hilhorst, J. Stat. Phys.53, 249 (1988).1565

Nothing moves a surface: vacancy mediated surface diffusion

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Nothing moves a surface: Vacancy mediated surface diffusion

The diffusion coefficient for copper terrace atoms was evaluated using the scanning tunneling microscopy (STM) technique. The monitoring of diffusion of surface atoms was studied using a low density of embedded indium atoms embedded within the first layer of a Cu(001) surface. It was found that surface vacancies were responsible for the mobility of the indium and terraces of low-index metal surfaces were not considered static, even at room temperature

Van Gastel, R.

Van Albada, S. B.

Van Saarloos, W.

Frenken, J. W.M.

Nothing moves a surface: vacancy mediated surface diffusion

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Leiden University Scholary Publications

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Leiden University Scholary Publications

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